Question: Solve for $x$ and $y$ using substitution. ${-5x-2y = 7}$ ${y = -2x-1}$
Solution: Since $y$ has already been solved for, substitute $-2x-1$ for $y$ in the first equation. ${-5x - 2}{(-2x-1)}{= 7}$ Simplify and solve for $x$ $-5x+4x + 2 = 7$ $-x+2 = 7$ $-x+2{-2} = 7{-2}$ $-x = 5$ $\dfrac{-x}{{-1}} = \dfrac{5}{{-1}}$ ${x = -5}$ Now that you know ${x = -5}$ , plug it back into $\thinspace {y = -2x-1}\thinspace$ to find $y$ ${y = -2}{(-5)}{ - 1}$ $y = 10 - 1$ $y = 9$ You can also plug ${x = -5}$ into $\thinspace {-5x-2y = 7}\thinspace$ and get the same answer for $y$ : ${-5}{(-5)}{ - 2y = 7}$ ${y = 9}$